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Tóvári Endre Journal Club 2013. márc. 8. „To bunch. Coherence and Indistinguishability of Single Electrons Emitted by Independent Sources. Science 339, 1054 (2013) Science 339, 1041 (2013). Two Indistinguishable Electrons Interfere in an Electronic Device. or not to bunch”.

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Tóvári Endre

Journal Club

2013. márc. 8.

„To bunch

Coherence and Indistinguishability

of Single Electrons Emitted by

Independent Sources

Science 339, 1054 (2013)

Science 339, 1041 (2013)

Two Indistinguishable Electrons

Interfere in an Electronic Device

or not to bunch”


Coherence and Indistinguishability

of Single Electrons Emitted by

Independent Sources

E. Bocquillon,1

V. Freulon,1

J.-M Berroir,1

P. Degiovanni,2

B. Plaçais,1

A. Cavanna,3

Y. Jin,3

G. Fève1*

1Laboratoire Pierre Aigrain, Ecole Normale Supérieure, CNRS

(UMR8551), Université Pierre et Marie Curie, Université Paris

Diderot, 24 rue Lhomond, 75231 Paris Cedex 05, France. 2Universitéde Lyon, Fédération de Physique AndréMarie Ampère,CNRS–Laboratoire de Physique de l’Ecole Normale Supérieurede Lyon 46 Allée d’Italie, 69364 Lyon Cedex 07, France.

3CNRS–Laboratoire de Photonique et de Nanostructures Route de Nozay, 91460 Marcoussis, France.

Two Indistinguishable Electrons

Interfere in an Electronic Device

Christian Schönenberger

Department of Physics, University of Basel



Hong-Ou-Mandel (HOM) dip

bunching

coincidence

Noise vs delay time

antibunching

Dip size and shape depends on wave packet overlap and width τe


Indistinguishable electrons needed

  • DC voltage:

  • continuous stream of electrons

  • but 2-e- interference cannot be interpreted as overlap between 2 single-particle wave packets

  • Triggered AC emitter: generating 1-e- wave packets at well-defined times

  • Realization:

  • Quantum dots: charge quantization

  • Quantum Hall regime: ballistic, 1D, chiral edge channels

  • AlGaAs/GaAs 2DEG

  • n=1,9x10-11 cm-2

  • µ=2,4x106 cm2/Vs

  • B=2,68T, ν=3 filling factor

  • QD addition energy Δ=1,4K

  • electron temperature 100 mK


  • QDot:

  • 2,1 GHz square wave on top gate:

  • p2p amplitude is the addition energy Δe- followed by h+

  • τe=58±7 ps average emission time

  • Tunnel coupling (with D=0,45±0,05 transmission) to an edge channel

  • Tunnel emission of single particles form a discrete dot level: exponential decay confirmed

τe: average emission time

emission trigger

2DEG

T=1/2


Probability of exiting at the same output:

Probability of different outputs:

(fermions)

τ>> τe: classical case

Perfectly indistinguishable states:


Normalized by the classical value e2f:

Antibunching with the thermal excitations: if ,

we must subtract the noise when both sources are switched off

(one source off)

antibunching of single indistinguishable fermions


Blue line:

τe=62±10 ps

γ=0,45±0,05 non-unit overlap

τ0=13±6 ps

Red line: Floquet scattering γ = 0.5, D1 = D2 = 0.4, Δ1 = Δ2 = 1.4K, and T = 100 mK.

( )

  • QDot:

  • τe=58±7 psa verage emission time

  • Tunnel coupling (with D=0,45±0,05 transmission) to an edge channel

  • 10 ps synchronization

  • Non-unit overlap γ:

  • possibly Δ/10 difference in QD levels

  • maybe τc≈100 ps coherence time:


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